shows that the Cartesian components of a given shell may have different normalization constants. In the HERMIT
integral code a single normalization is chosen for each shell by ignoring \(F_{ijk}\) meaning that Cartesian
Gaussians are normalized to

In practice this means that s- and p-functions are normalized to one. So are \(d110\), \(d101\) and
\(d011\), whereas \(d200\), \(d020\) and \(d002\) are normalized to three. \(f111\) is
normalized to one, \(f210\), \(f201\), \(f120\), \(f102\) and \(f012\) are normalized to
three, and \(f300\), \(f030\) and \(f003\) are normalized to 15.

For given \(l\) there are \(\frac{1}{2}\left(l+2\right)\left(l+1\right)\)\(\left(2l+1\right)\) spherical Gaussians.
The latter basis functions therefore provide more compact basis set expansions. However, in 4-component relativistic calculations
the use of spherical Gaussians is somewhat more complicated since the coupling of large and small component basis functions needs
to be taken into account.

Kinetic balance corresponds to the non-relativistic limit of the exact coupling of large and small component basis functions for
positive-energy orbitals. Starting from the radial function of a large component spherical Gaussian basis function one obtains